For questions about geometric shapes, congruences, similarities, transformations, as well as the properties of classes of figures, points, lines, angles.

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2
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1answer
77 views

Have you seen this golden ratio construction before? Three squares (or just two) and circle. Geogebra gives PHI or 1.6180.. exactly

Note this golden ratio construction has been dramatically updated here with numerous golden harmonies: A Golden Ratio Symphony! Why so many golden ratios in a relatively simple golden ratio ...
0
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0answers
9 views

What is an orthogonal monometric system?

I am reading a journal paper. In that I have chosen a flat slab as a reference geometry for some object. Then they have placed a orthogonal monometric system x,y,z with the plan of xy coinciding with ...
1
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0answers
48 views

Surface area of cone without calculus

Let $l$ be the length of a cone's lateral and $r$ be the radius of its base. The cone's surface area (excluding the base) is $\pi rl$. Briefly googling, most proofs I see simply claim that if you ...
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0answers
19 views

percentage of regular shapes surface area visible in 3d

inspired by How many faces of a solid can one "see"? at first I thought 3 faces of a cube and half a sphere seem opposite extremes both with 50% surface area visible. then I considered a ...
3
votes
1answer
20 views

Number of faces visible in different dimensions [duplicate]

In 3D, if I look at a cube, at most I can see three faces at one time from any given perspective, e.g. by looking at a corner dead on. In 2D, if I look at a square and my perspective is in the plane ...
1
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1answer
19 views

Proof of the reflective property of the ellipese

I'm trying to prove the reflection property of the ellipses for an optics problem. The property is that that a ray of light originated at one of the ellipse's foci reflects in such a way to pass ...
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4answers
46 views

Is this a correct way to solve this high school coordinate geometry question?

Here's the question: Given point $A$: $(-3;-1)$ Given point $B$: $(3;7)$ Given point $Z$: $(x;0)$ Find the $x$ coordinate of point $Z$ so that the angle of view of AB segment is $90$ ...
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0answers
14 views

Given bases of a right trapezoid with right-angled diagonals, find area [closed]

Find the area of a right trapezoid with bases 18 and 32 which has diagonals that form a right angle.
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2answers
30 views

How to find intersections of sine and cosine functions with $X$ axis

I've been struggling with this question for a few days, because I've been able to find the said intersections, but based on suppositions, rather than on mathematical process. For example, if I have ...
0
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1answer
27 views

Surfaces of revolution which are also ruled surfaces.

I have been struggling to solve the following problem: "Determine all surfaces of revolution which are also ruled surfaces (in $\mathbb{R}^3$)." Local parameterisations of ruled surfaces take the ...
-1
votes
3answers
79 views

How to calculate the distance between two points on a circle in degrees [closed]

I've been trying to figure this out for several hours now and am having trouble finding the right solution. Given two points on a circle and the radius of the circle I need to calculate the distance ...
0
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1answer
16 views

Finding 3rd circle's coordinate of particular radius given 2 circles coordinate, circles touch externally

Given circle say A,B,C where each of them touches each other externally . We are given radius of all 3 circles. We are also given 2-D coordinates of centre of B,C ,we need to compute coordinates of A. ...
3
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1answer
30 views

Is there a common name for solids where $V = h \cdot A_t = h \cdot A_b$

I'm trying to find a name which describes all solids which have these properties: $h = height$ $A_{t} = top\ area$ $A_{b} = base\ area$ $A_{t} = A_{b}$ $V = h \cdot A_t = h \cdot A_b$ Examples ...
2
votes
1answer
29 views

Is there some relationship for all points on a rectangle?

For a line in 3D space, you can know that for each P on the line with endpoints A and B and length L, it holds that ||P-A|| + ||P-B|| = L My question is: is there a similar expression for points on ...
-2
votes
1answer
27 views

Given the lengths of perpendicular diagonals in a trapezoid, find the length of the trapezoid's median [closed]

The diagonals of a trapezoid are perpendicular and have lengths 8 and 10. Find the length of the median of the trapezoid. Please Help Please Include A solution so I can understand I know that ...
-1
votes
2answers
50 views

Find the length of the median of a trapezoid from the lengths of its diagonals? [closed]

Is there a formula to find the length of the median of a trapezoid given the lengths of its diagonals?
0
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3answers
39 views

Geometry Question Help

The bases of trapezoid $ABCD$ are $\overline{AB}$ and $\overline{CD}$. We are given that $CD = 8$, $AD = BC = 7$, and $BD = 9$. Find the area of the trapezoid.
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0answers
24 views

A Plucker style proof of Monge's Theorem

Plucker, famously, proved Pascal's theorem for all conics at once, using the technique described in the answer here. I was wondering if there was a proof for Monge's Theorem using the above ...
1
vote
1answer
18 views

Perform a rotation in 3D world

I got a character at some point $A$ facing to point $O$ that is equal to $(0,0,0)$, then I move it to point $B$ and I want to rotate him to face point $O$. Since this is 3D world I think that I need ...
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0answers
35 views

Number theory/calculus/algebra etc. equivalents of Euclid's Elements?

Anybody know any books that tackle mathematical topics in a deductive, axiomatic structure akin to Euclid's Elements? Thanks.
0
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1answer
31 views

Geometry including semicircle and arc length

This is a question in the Princeton online test of GRE general book. I got it wrong, but even when I looked at the answer I find it difficult to understand how the answer is obtained. In the ...
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0answers
33 views

Finding a point coordinate given some distance restrictions relative to other points

I want to find the solution space of coordinates for point $p$ that satisfies the following system: $$ \begin{cases} [distance(p,a) - distance(p,b)] = k_1\\ [distance(p,c) - distance(p,d)] = k_2 ...
0
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1answer
54 views

Sine law and circumscribed circle

How is $\frac{a}{\sin(A)}=2R$ (where $R$ is the radius) derived?
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3answers
74 views

How to show that any rectangle in ellipse must be oriented parallel to axes?

A problem which is often given as an exercise for students learning about calculus and finding extrema, is to find maximal possible area of a rectangle inside an ellipse. Such question was asked, for ...
4
votes
1answer
20 views

parallelograms formed by horizontal and vertical lines

Can anyone help me with this problem or give me an hint on how to solve it? I don't think I do not understand this problem well. How can two horizontal and vertical lines create 360 parallelograms? ...
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2answers
64 views

New Golden Ratio Construct with Geogebra using Square and Triangle with Same Base Width. Geometric proof of golden section?

The below construct of the golden ratio, based on the ratio of segment c to segemnt b, is so very close to PHI. Geogebra gives the value of 1.61957 instead of 1.61803. Might anyone have any insight ...
0
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1answer
32 views

Getting the coordinates of the center of a circle bisecting two other circles.

We have circles $C_1$ and $C_2$ with centers $(-d,0)$ and $(d,0)$, radii $a_1<d$ and $a_2<d$ respectively. If circle $D$ with radius $r$ (and with centre not necessarily on the x-axis) bisects ...
0
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1answer
42 views

Geometric interpretation of the ratio of the sides of a triangle.

In right triangle trigonometry, the sine of an angle $A$ is defined as the ratio of two lengths, the opposite leg $a$ and the hypotenuse $c$, that's to say, $\sin A= \frac{a}{c}$? My question is: ...
2
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0answers
22 views

Simplification of Levi-Civita in an orthonormal frame

I have been struggling to understand how picking an orthonormal frame for the tangent space of a Riemann surface with local coordinates ${x_1,x_2}$ simplifies the matrix of one forms associated to its ...
0
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0answers
26 views

Finding the dimensions of a stair on a round staircase

I wasn't too sure how to word this, but I'm going to do my best. Today, I was given a challenge math problem by my teacher. It was off the top of his head and riddled with errors, forcing me to set ...
0
votes
1answer
58 views

What is the number of interior faces adjacent to an interior vertex in a triangulation in $\mathbb{R}^3$?

Let $\Omega$ be a polygonal domain in $\mathbb{R}^3$. Assume $\Omega$ is partitioned into tetrahedra using the most common admissible triangulation, that is, roughly speaking, two adjacent tetrahedra ...
0
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1answer
24 views

What curves have a closed-form formula for projecting a point onto them in multiple dimensions?

What curves have a closed-form formula for projecting a point onto them in multiple dimensions? For example, give a simple, straight line $$ c(t) = v t $$ where $v\in\mathbb{R}^m$ and ...
0
votes
1answer
27 views

Scalar product is 0 in any triangle

How can we prove that the following scalar product relation holds in any triangle? $$\left [-\overrightarrow{AB}\tan B (\tan A +2\tan C)+\overrightarrow{AC}\tan C (\tan A+2\tan B)\right ]\cdot \left ...
1
vote
1answer
69 views

Area of Pentagon question

Suppose that a regular pentagon circumscribes a circle of radius $r$. Show that the area of the pentagon is $5r^2\tan(36°)$. I know that the area of a triangle is $\frac{1}{2}bh$, where $b$ is the ...
0
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0answers
31 views

Approximate area of overlap of two rotated rectangles

I need to estimate the overlap ratio of two rectangles, each one with arbitrary size and orientation. I know how to perform the exact computation, using the Sutherland-Hodgman algorithm, which can be ...
1
vote
1answer
24 views

Understanding Drawing Scale

I'm a little confused about reading scales. I do understand that if I see a scale of 1:30, that means that the object is 30 times smaller then in real world or 30:1 where the object is 30 time bigger ...
0
votes
1answer
22 views

Support Vector machine & Support Vector

I had gone through several example of SVM and I see one starts explaining SVM by picking up the support vectors upfront (like this https://www.youtube.com/watch?v=1NxnPkZM9bc). Basically those vectors ...
2
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0answers
25 views

Connection between the area of a n-sphere and the Riemann zeta function?

The Riemann Xi-Function is defined as $$ \xi(s) = \tfrac{1}{2} s(s-1) \pi^{-s/2} \Gamma\left(\tfrac{1}{2} s\right) \zeta(s) $$ and it satisfies the reflection formula $$ \xi(s) = \xi(1-s). $$ But the ...
0
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2answers
38 views

Finding Launch Angle for Two Projectile Collision

I'm trying to figure out the general equation for calculating the launch angle of one projectile required when trying to find a collision between that projectile and another. For the equation I've ...
0
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2answers
40 views

Find angle of a right triangle.

Ok, so this question is from a practice exam. Looks very simple and basic, but I'm not very good at math, so I'm having trouble setting up the problem. One acute angle of a right triangle is not ...
4
votes
1answer
35 views

Computing volume of concave polyhedron

I have a circular grid with points uniformly distributed throughout it. See this: Each point has some nonnegative height assigned to it (i.e. height can be 0 on up). I'm trying to accurately ...
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1answer
15 views

Find range of values for a square's area.

This is question is from my practice final exam. The perimeter of a square is to be between 20 meters and 60 meters. What is the range of values for its area?
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0answers
37 views

Maximum Distance to the Center and Foci for a Point Inside an Ellipse

Given an ellipse with foci $f_1$ and $f_2$, major axis $M$, minor axis $m$ and center $c$ how could I find the maximum distance that a point inside the ellipse can be to $f_1$, $f_2$ or $c$ such that ...
0
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1answer
47 views

How can you fill a square whit trapezoids? [closed]

Good day, My question is how do you fill a square whit trapezoids that dont have a 90 degrees angle. Thanks for help.
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0answers
23 views

Area of a shadow made from a spherical balloon?

A light at position $(0,0,8)$ shines down on a spherical balloon of radius $\sqrt5$ centered at $(3,4,3)$. Find the area of the shadow which is cast on the xy-plane. The shadow is an ellipse and the ...
2
votes
1answer
34 views

parallelogram diagonals in a relationship with basic geometry

This was a question in my textbook for homework a while ago but not even the teacher can find the solution using only basic geometry (further rules below). Basic only since it's in the section where ...
3
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0answers
19 views

Do $(1+\varepsilon)$- bilipschitz maps preserve angles?

Let $f:\mathbb{R}^2 \rightarrow \mathbb{R}^2$ be a bilipschitz map such that $$ \frac{1}{1+\varepsilon} d(x,y) \leq d(f(x),f(y)) \leq (1+ \varepsilon) d(x,y) $$ for some $\varepsilon>0$ and the ...
0
votes
3answers
37 views

Finding side of triangle given central angle and radius of the described circle

Given $\triangle ABC$, is described around $k(O; R)$ and $\angle AOC = 120$, $\angle CAB=\alpha$ find$AB$. The answer is $2R\sin(120-\alpha)$ However I don't know how to prove it. Here is drawing:
2
votes
1answer
51 views

Triangle with sides less than $1$.

If the triangle sides are less than $1$, what is the maximum value of the area? I'm in doubt between using $A=\frac12\cdot 1\cdot 1\cdot \sin a$, or using heron's formula.
0
votes
1answer
26 views

How big do squares need to be to fit a box, tesselating, with minimal remainder?

A geometry question that I feel utterly defeated by. I'm trying to design a responsive user interface that efficiently fits a variable number of square elements on a screen, by adjusting the size of ...